Multiple-input Multiple-output Channel Estimation Research Articles

An adaptive compressive sensing method on hybrid-field channel estimation for a massive MIMO system

Massive MIMO (Multiple-input-multiple output), crucial for 5 G and Beyond 5 G (B5G) networks, faces challenges with terahertz frequencies in B5G as the communication shifts from far-field to near-field. This shift disrupts traditional Massive MIMO channel estimation, leading to increased pilot overhead and limited performance. The current study used the hybrid-field orthogonal matching pursuit (HF-OMP) algorithm from the compressive sensing (CS) framework to estimate the channel with scatters from both far-field and near-field. The method, however, needs more flexibility regarding scatter location in the field of interest. Also, the usage of HF-OMP under a single measurement vector (SMV) scheme limits the overall performance of the existing method. To address these, we have proposed an adaptive hybrid-field simultaneous-OMP algorithm under multiple measurement vector (MMV) of the CS framework which selects multiple atoms having common support within a single iteration. This innovative approach tackles channel estimation for both far-field and near-field scatters while adapting to their varying distributions. Compared to classical methods, simulations show the new algorithm achieves up to a 14 % improvement in normalized mean square error within a 0 dB to 10 dB signal-to-noise ratio range. This translates to significant reductions in pilot overhead and enhanced channel reliability, paving the way for more efficient and robust wireless networks in the future.

Exact Analysis of MIMO Channel Estimation Based on Superimposed Training

In this paper, channel estimation capabilities of a multiple-input multiple-output (MIMO) system using superimposed training sequences are investigated. A new expression for estimation-error variance is derived. It is shown that the training sequences must be balanced and must have specific correlation properties. The latter are required only in a specific zone. Sequences that satisfy these criteria exist and are referred to as zero-correlation zone (ZCZ) solutions. Consequently, by using balanced ZCZ sequences, harmful direct current (DC) offset can be removed. Owing to their zero-cross correlation, interference from other transmitting antennas may be eliminated. Furthermore, a closed-form expression of the estimation-error variance can be obtained due to their impulse-like autocorrelation. To increase the number of antennas in the MIMO system, a new construction of ZCZ sequence set is proposed, in which all sequences are balanced

A low-complexity algorithm based on variational Bayesian inference for MIMO channel estimation

With an increase in the number of transmitters in multiple-input multiple-output (MIMO) communication systems, there is a cubic rise in the computational complexity of the traditional sparse Bayesian learning (SBL) channel estimation algorithm. While various algorithms are effective for single-input single-output (SISO) systems, they are not suitable for the MIMO scenario. This paper introduces a MIMO channel estimation algorithm based on variational Bayesian inference (VBI) by assuming the independence of the variational distribution among different channels. The high-dimensional channel vectors estimated in the conventional MIMO-SBL algorithm are decomposed into multiple parallel low-dimensional channel vectors with different sparsity using VBI. Consequently, the complexity exhibits a linear relationship with the number of transmitters, as demonstrated through numerical analysis. Simulations confirm the improved estimation accuracy of the MIMO-VBI algorithm. Experimental results reveal that MIMO systems can achieve lower bit error rates using the MIMO-VBI algorithm, with reduced runtime for channel lengths exceeding 100 symbols.

Massive multiple-input multiple-output channel estimation under hardware and channel impairments

Hardware problems are the most detrimental issues to channel estimates in wireless communication systems. Because of the enormous number of antennas at the base station (BS) in cellular massive multiple-input multiple-output (MIMO) systems and because one radio frequency (RF) chain per antenna is required, hardware impairments in such systems will be quite severe. Many research publications have used a quality-cost tradeoff to adjust for RF unit hardware issues. In this study, we have taken a different approach by reducing the error floor caused by impairments in the predicted channels. Here are two steps to remedy the problem. In phase 1, a single active user channel in a single cell was calculated statistically rather than parametrically. In phase 2, a convex optimization approach was used to regularize the estimated channel in phase 1 to reduce error and provide a robust channel estimate. The results of our proposed procedure are measured by the normalized minimum mean squared error (NMSE) versus a range from the effective signal-to-noise ratio, and it shows a significant reduction (nearly one order of magnitude) in the error floor as compared with the conventional one, especially at high signal-to-noise ratio (SNR) in the range of (20 dB-30 dB). Simulation results were extracted in MATLAB R2020a.

Multivariate and Global Particle Swarm Algorithm Optimization in mmWave Massive MIMO for Angle Domain Channel Estimation

Exploitation of massive Multiple-Input Multiple-Output gains for downlink transmission in Millimetre Wave Systems comes at the expense of obtaining accurate channel estimation and computing complexity. Moreover, the fundamental task of massive Multiple-Input Multiple-Output channel estimation is to exploit the characteristics of the channel and sparsity of these multi-antennas systems to simplify complicated spatial structures. We tackle the channel estimation problem in constructing angle domain channel model with multivariate optimization. In the proposed global particle swarm optimization for angle domain aided scheme, the channel estimation design is decoupled into two parts The simulation results are provided to demonstrate the superior performance of the proposed algorithm over the traditional CS-based channel estimation methods.

A fast gridless mmWave full-dimensional MIMO channel estimation method

Most existing channel estimation methods for millimeter-wave (mmWave) multiple-input multiple-output (MIMO) communication systems focus on linear arrays rather than planar arrays since discretizing the high-dimensional angle space in planar array scenario brings in high computations. In this paper, we consider the channel estimation problem for mmWave full-dimensional MIMO system where the base station (BS) and user equipment (UE) are equipped with planar arrays. We first propose an atomic ℓ0 norm based optimization problem to find the angle estimates and then transfer the problem into a solvable semidefinite programming (SDP). We next propose a computationally efficient algorithm to solve the SDP rather than employing existing standard solvers. Compared with the grid based methods which require discretizing the angle space, our method avoids angle discretization which brings in huge computations. Various simulations show that our method is able to provide satisfying channel estimation performance while is also computationally efficient.

Joint CFO and channel estimation using pilot aided interpolation for high performance MIMO-OFDM

ABSTRACT Multiple Input Multiple Output (MIMO) system with orthogonal frequency division multiplexing (OFDM) is a promising physical layer candidate for the current and future wireless standards. MIMO increases system throughput while OFDM maximizes spectrum efficiency. To reduce the impacts of frequency selective fading and increase the capacity, MIMO requires precise channel state information (CSI). The presence of carrier frequency offset (CFO) introduces intercarrier interference (ICI) among the subcarriers which degrades the system performance. MIMO channel estimation is done under the assumption of perfect frequency synchronisation between the transmitter and receiver, or zero CFO. However, such an assumption is incorrect for time-varying and frequency-selective wireless channels, and the presence of CFO has an impact on channel estimation accuracy. In the existing methods, CFO and channel estimations are carried out independently using separate training sequences which reduces the spectral efficiency. As a result, the pilot aided interpolation approach is proposed in this paper for the joint estimate and compensation of CFO and channel effects using the same set of pilot tones. Theresults show that the proposed method offers precise CFO and channel estimation which improves the bit error rate performance and carrier to interference power ratio (CIR) of MIMO-OFDM system.

Federated Learning for Channel Estimation in Conventional and RIS-Assisted Massive MIMO

Machine learning (ML) has attracted a great research interest for physical layer design problems, such as channel estimation, thanks to its low complexity and robustness. Channel estimation via ML requires model training on a dataset, which usually includes the received pilot signals as input and channel data as output. In previous works, model training is mostly done via centralized learning (CL), where the whole training dataset is collected from the users at the base station (BS). This approach introduces huge communication overhead for data collection. In this paper, to address this challenge, we propose a federated learning (FL) framework for channel estimation. We design a convolutional neural network (CNN) trained on the local datasets of the users without sending them to the BS. We develop FL-based channel estimation schemes for both conventional and RIS (intelligent reflecting surface) assisted massive MIMO (multiple-input multiple-output) systems, where a single CNN is trained for two different datasets for both scenarios. We evaluate the performance for noisy and quantized model transmission and show that the proposed approach provides approximately 16 times lower overhead than CL, while maintaining satisfactory performance close to CL. Furthermore, the proposed architecture exhibits lower estimation error than the state-of-the-art ML-based schemes.

A Family of Deep Learning Architectures for Channel Estimation and Hybrid Beamforming in Multi-Carrier mm-Wave Massive MIMO

Hybrid analog and digital beamforming transceivers are instrumental in addressing the challenge of expensive hardware and high training overheads in the next generation millimeter-wave (mm-Wave) massive MIMO (multiple-input multiple-output) systems. However, lack of fully digital beamforming in hybrid architectures and short coherence times at mm-Wave impose additional constraints on the channel estimation. Prior works on addressing these challenges have focused largely on narrowband channels wherein optimization-based or greedy algorithms were employed to derive hybrid beamformers. In this paper, we introduce a deep learning (DL) approach for channel estimation and hybrid beamforming for frequency-selective, wideband mm-Wave systems. In particular, we consider a massive MIMO Orthogonal Frequency Division Multiplexing (MIMO-OFDM) system and propose three different DL frameworks comprising convolutional neural networks (CNNs), which accept the raw data of received signal as input and yield channel estimates and the hybrid beamformers at the output. We also introduce both offline and online prediction schemes. Numerical experiments demonstrate that, compared to the current state-of-the-art optimization and DL methods, our approach provides higher spectral efficiency, lesser computational cost and fewer number of pilot signals, and higher tolerance against the deviations in the received pilot data, corrupted channel matrix, and propagation environment.

Performance analysis of a millimeter wave MIMO channel estimation method in an embedded multi-core processor

The emerging Multi-Processor System-on-Chip (MPSoC) technology, which combines heterogeneous computing with the high performance of field programmable gate arrays (FPGA), is a promising platform for a large number of applications, including wireless communications and vehicular technology. In this specific application context, when multiple-input multiple-output (MIMO) scenarios are considered, the system usually has to manage a large number of communication links among sensors and antennas involving different vehicles and users. Millimeter wave (mmWave) communications are one of the key technology enablers toward achieving high data rates in beyond 5G systems (B5G). Communication at these frequency bands usually involves the use of large antenna arrays, often requiring high computational resources. One of the candidate platforms able to manage a huge number of communications is the Xilinx Zynq UltraScale+ EG Heterogeneous MPSoC, which is composed of a dual-core Cortex-R5, a quad-core ARM Cortex-A53, a graphics processing unit (GPU) and a high-end FPGA. This work analyzes the computational performance that requires a recent mmWave MIMO channel estimation algorithm in a platform of this kind. As a first approach, we will focus our work on the performance that can be achieved via the quad-core ARM Cortex-A53. To this end, we will use the libraries for numerical algebra (BLAS and LAPACK). The results show that our reference implementation is able to manage a large MIMO communication system with 256 antennas without exhausting platform resources.

Deep Transfer Learning for Site-Specific Channel Estimation in Low-Resolution mmWave MIMO

We consider the problem of channel estimation in low-resolution multiple-input multiple-output (MIMO) systems operating at millimeter wave (mmWave) and present a deep transfer learning (DTL) approach that exploits previously trained models to speed up site adaptation. The proposed model is composed of a feature extractor and a regressor, with only the regressor requiring training for the new environment. The DTL approach is evaluated using two 3D scenarios where ray-tracing is performed to generate the mmWave MIMO channels used in the simulations. Under the defined testing setup, the proposed DTL approach can reduce the computational cost of the training stage without decreasing the estimation accuracy.

Deep Task-Based Quantization.

Quantizers play a critical role in digital signal processing systems. Recent works have shown that the performance of acquiring multiple analog signals using scalar analog-to-digital converters (ADCs) can be significantly improved by processing the signals prior to quantization. However, the design of such hybrid quantizers is quite complex, and their implementation requires complete knowledge of the statistical model of the analog signal. In this work we design data-driven task-oriented quantization systems with scalar ADCs, which determine their analog-to-digital mapping using deep learning tools. These mappings are designed to facilitate the task of recovering underlying information from the quantized signals. By using deep learning, we circumvent the need to explicitly recover the system model and to find the proper quantization rule for it. Our main target application is multiple-input multiple-output (MIMO) communication receivers, which simultaneously acquire a set of analog signals, and are commonly subject to constraints on the number of bits. Our results indicate that, in a MIMO channel estimation setup, the proposed deep task-bask quantizer is capable of approaching the optimal performance limits dictated by indirect rate-distortion theory, achievable using vector quantizers and requiring complete knowledge of the underlying statistical model. Furthermore, for a symbol detection scenario, it is demonstrated that the proposed approach can realize reliable bit-efficient hybrid MIMO receivers capable of setting their quantization rule in light of the task.

Channel Estimation for 6G V2X Hybrid Systems Using Multi-Vehicular Learning

Channel estimation for hybrid Multiple Input Multiple Output (MIMO) systems at Millimeter-Waves/sub-THz is a fundamental, despite challenging, prerequisite for an efficient design of hybrid MIMO precoding/combining. Most works propose sequential search algorithms, e.g., Compressive Sensing (CS), that are most suited to static channels and consequently cannot apply to highly dynamic scenarios such as Vehicle-to-Everything (V2X). To address the latter ones, we leverage recurrent vehicle passages to design a novel Multi Vehicular (MV) hybrid MIMO channel estimation suited for Vehicle-to-Infrastructure (V2I) and Vehicle-to-Network (V2N) systems. Our approach derives the analog precoder/combiner through a MV beam alignment procedure. For the digital precoder/combiner, we adapt the Low-Rank (LR) channel estimation method to learn the position-dependent eigenmodes of the received digital signal (after beamforming), which is used to estimate the compressed channel in the communication phase. Extensive numerical simulations, obtained with ray-tracing channel data and realistic vehicle trajectories, demonstrate the benefits of our solution in terms of both achievable spectral efficiency and mean square error compared to the unconstrained maximum likelihood estimate of the compressed digital channel, making it suitable for both 5G and future 6G systems. Most notably, in some scenarios, we obtain the performance of the optimal fully digital systems.

MIMO channel estimation with arbitrary angle of arrival incident power spectrum for wireless communications

This study proposes an approximate algorithm for the arbitrary angle of arrival (AoA) incident power spectrum in wireless environments. The approach expands approximate algorithms for small angles to the large-angle AoA PDF. To achieve this, the fading correlation of wireless channels is calculated and derived for various theoretical fittings and measured data. Then, the multiple-input multiple-output (MIMO) channel model is reconstructed for special environments using spatial fading correlation (SFC). Following this, the approximate algorithm and its complexity are investigated in depth in the SFC of multi-antenna arrays with small AoA angles under uniform, Gaussian, and Laplacian distributions, which can function in macrocell and microcell environments. Further, the closed form formulas for SFC are derived for the small angle spread of incident signals. The formulas are extended to simulate these cases with large angle spreads, which result in an increasing calculation complexity, particularly for the actual measured results. The selection of the number of samples and the weighting coefficient in the large angle spreads and its fitting accuracy are considered in detail. Based on this relationship, the properties of the temporal correlation and channel of the MIMO uniform linear array are studied and discussed.

Enhanced Tensor-Based Joint Channel and Symbol Estimation in Dual-Hop MIMO Relaying Systems

In this letter, an enhanced alternating least squares (EALS) algorithm for joint channel and symbol estimation is proposed in a dual-hop multiple input multiple output (MIMO) relaying communication system based on a simplified Khatri-Rao space-time (KRST) coding at the source node. The proposed method exploits the parallel factor (PARAFAC) and PARATUCK2 models at the relay node and the destination node, respectively. Exploiting the structure of these tensor models, we present an iterative alternating estimation scheme using optimized step size factors for accelerated convergence and lower overall complexity compared to conventional approaches. Identifiability conditions and computational complexity are analyzed, and simulation results are provided to corroborate the effectiveness of the proposed algorithm.

Semi-blind joint channel estimation and data detection on sphere manifold for MIMO with high-order QAM signaling

A low-complexity semi-blind scheme is proposed for joint channel estimation and data detection on sphere manifold for multiple-input multiple-output (MIMO) systems with high-order quadrature amplitude modulation signaling. Specifically, the optimal channel estimator is expressed in the least squares form in terms of the received signals and unknown transmitted data, and by splitting the channel and transmitted data into their real parts and imaginary parts, the data detection becomes a problem defined on a scaled sphere manifold in the real domain. Our semi-blind algorithm consists of three stages: (i) a few training symbols are employed to provide a rough initial MIMO channel estimate which in turn yields the initial zero-forcing (ZF) estimate of data samples; (ii) the Riemannian conjugate gradient algorithm is used to estimate the data samples in real domain, and the detected data samples are used to estimate the final MIMO channel matrix; and (iii) the final ZF data detection is carried out based on the final MIMO channel estimate. In particular, we present the first order Riemannian geometry of the sphere manifold which is utilized in the Riemannian conjugate gradient algorithm for solving (ii). Simulation results are employed to demonstrate the effectiveness of the proposed approach.

Exploiting Spatial–Temporal Joint Sparsity for Underwater Acoustic Multiple-Input–Multiple-Output Communications

Multiple-input–multiple-output (MIMO) system offers a promising way for high data rate communication over bandwidth-limited underwater acoustic channels. However, MIMO communication not only suffers from intersymbol interference, but also introduces the additional co-channel interference, which brings challenge for underwater acoustic MIMO channel estimation and for channel equalization. In this article, we propose novel interference cancellation (IC) methods for handling this co-channel interference problem in the design of both channel estimation and channel equalization. Our method for channel estimation utilizes the spatial joint sparsity and the temporal joint sparsity in the multipath structure to estimate sparse channels with common delays under distributed compressed sensing framework. In this way, we enhance channel estimates with common delays, thus, suppress co-channel interference. Meanwhile, to address the case of multipath arrivals with different delays, which are estimated as noise under simultaneous orthogonal matching pursuit (SOMP) algorithm, we introduce forward–reverse strategy to SOMP algorithm, which is referred to as the FRSOMP algorithm. Our proposed FRSOMP algorithm performs the SOMP algorithm to achieve the initial channel estimates, performs the forward-add process, which attempts to add promising candidates into support sets, and performs the reverse-fetch process to check if the candidates in the support set are retained or removed. The purpose of channel estimation is to directly calculate the filter coefficients for channel-estimation-based decision feedback equalization (CE-DFE). In this article, we also propose a novel CE-DFE receiver with IC component. We design IC filters based on the traditional CE-DFE, and we derive the coefficients of the feedforward filters, feedback filters, and IC filters based on the channel estimate metric obtained by the FRSOMP algorithm, so the co-channel interference will be suppressed both in channel estimation and channel equalization. We demonstrate the performance of our approach by numerical simulation, lake experiment, and sea experiment. Results are provided to demonstrate the effectiveness of the proposed methods, which show that the proposed methods obtain higher output signal-to-noise ratio, lower bit error rate, and more separated constellations compared with the traditional compressed sensing channel estimation method and the traditional CE-DFE method.

Impact of Doppler shift error on least‐squares MIMO channel estimation for high‐speed railway

Owing to the availability of Doppler shift measurement and the existence of dominant line-of-sight (LOS) path in high-speed railway (HSR) communications, Doppler shift is often pre-compensated on the received signal before performing further processing. In this study, the authors address the impact of erroneous Doppler shift measurement on the tracking performance of least-squares multiple-input multiple-output (MIMO) channel estimation for HSR. The closed-form tracking mean-square error (MSE) is derived over time-varying Rician fading channel assuming Gaussian distributed Doppler shift measurement. By transforming the Gaussian distributed measurement into its characteristic function and performing approximations with practical considerations, the tracking MSE of the approach with Doppler shift pre-compensation is written as a function of that with no pre-compensation, contributed from the previous research. Accordingly, they are able to develop a simple relation between MSE gain and MSE loss for channels with dominant LOS path. It is revealed that erroneous Doppler shift measurement impacts stronger LOS or faster time-varying channel more severely. However, if the measurement is perfect, the presence of a dominant LOS path provides tremendous gain approximately equal to the Rician factor in high signal-to-noise ratio (SNR) regime.

Channel Estimation in Massive MIMO Under Hardware Non-Linearities: Bayesian Methods Versus Deep Learning

This paper considers the joint impact of non-linear hardware impairments at the base station (BS) and user equipments (UEs) on the uplink performance of single-cell massive MIMO (multiple-input multiple-output) in practical Rician fading environments. First, Bussgang decomposition-based effective channels and distortion characteristics are analytically derived and the spectral efficiency (SE) achieved by several receivers are explored for third-order non-linearities. Next, two deep feedforward neural networks are designed and trained to estimate the effective channels and the distortion variance at each BS antenna, which are used in signal detection. We compare the performance of the proposed methods with state-of-the-art distortion-aware and -unaware Bayesian linear minimum mean-squared error (LMMSE) estimators. The proposed deep learning approach improves the estimation quality by exploiting impairment characteristics, while LMMSE methods treat distortion as noise. Using the data generated by the derived effective channels for general order of non-linearities at both the BS and UEs, it is shown that the deep learning-based estimator provides better estimates of the effective channels also for non-linearities more than order three.

Cooperative Relative UAV Attitude Estimation Using DoA and RF Polarization

Relative unmanned aerial vehicle attitude is estimated using only on-board radio-frequency signaling. The method uses a direction-of-arrival (DoA) vector estimate to determine two degrees-of-freedom (DoFs), a polarimetric narrowband multiple-input multiple-output (MIMO) channel estimate to specify the third DoF to within a 180° ambiguity, and one of the several potential methods for ambiguity resolution. Simulation results demonstrate that the method accurately determines aircraft attitude, with errors proportional to DoA and MIMO channel estimate errors. This approach is useful for cooperative navigation when external navigation aids are not available, such as in GPS-denied environments.